The Master Equation and the Convergence Problem in Mean Field Games:
Gespeichert in:
| Beteiligte Personen: | , , , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Princeton and Oxford
Princeton University Press
2019
|
| Schriftenreihe: | Annals of mathematics studies
Number 201 |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031488139&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Enthält Literaturverzeichnis Seite 203-209 und Index |
| Umfang: | x, 212 Seiten |
| ISBN: | 9780691190716 9780691190709 |
Internformat
MARC
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| 245 | 1 | 0 | |a The Master Equation and the Convergence Problem in Mean Field Games |c Pierre Cardaliaguet, François Delarue, Jean-Michel Lasry, Pierre-Louis Lions |
| 264 | 1 | |a Princeton and Oxford |b Princeton University Press |c 2019 | |
| 264 | 4 | |c © 2019 | |
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| 700 | 1 | |a Lasry, Jean-Michel |0 (DE-588)171091930 |4 aut | |
| 700 | 1 | |a Lions, Pierre-Louis |d 1956- |0 (DE-588)1038560152 |4 aut | |
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Datensatz im Suchindex
| _version_ | 1819308065189527552 |
|---|---|
| adam_text | Contents
Preface vii
1 Introduction 1
1 1 From the Nash System to the Master Equation 1
1 2 Informal Derivation of the Master Equation 19
2 Presentation of the Main Results 28
2 1 Notations 28
2 2 Derivatives 30
2 3 Assumptions 36
2 4 Statement of the Main Results 38
3 A Starter: The First-Order Master Equation 48
3 1 Space Regularity of U 49
3 2 Lipschitz Continuity of U 53
3 3 Estimates on a Linear System 60
3 4 Differentiability of U with Respect to the Measure 67
3 5 Proof of the Solvability of the First-Order Master Equation 72
3 6 Lipschitz Continuity of with Respect to m 75
3 7 Link with the Optimal Control of the Fokker-Planck Equation 77
4 Mean Field Game System with a Common Noise 85
4 1 Stochastic Fokker-Planck/Hamilton-Jacobi-
Bellman System 86
4 2 Probabilistic Setup 89
4 3 Solvability of the Stochastic Fokker-Planck/
Hamilton-Jacobi-Bellman System 89
4 4 Linearization 112
5 The Second-Order Master Equation 128
5 1 Construction of the Solution 128
5 2 First-Order Differentiability 132
5 3 Second-Order Differentiability 141
5 4 Derivation of the Master Equation 150
5 5 Well-Posedness of the Stochastic MFG System 155
VI
CONTENTS
6 Convergence of the Nash System
6 1 Finite Dimensional Projections of U
6 2 Convergence
6 3 Propagation of Chaos
159
160
166
172
A Appendix
A l Link with the Derivative on the Space of Random Variables
A 2 Technical Remarks on Derivatives
A 3 Various Forms of Itö’s Formula
175
175
183
189
References
Index
203
|
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| author | Cardaliaguet, Pierre Delarue, François 1976- Lasry, Jean-Michel Lions, Pierre-Louis 1956- |
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| bvnumber | BV046107453 |
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| discipline | Mathematik |
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| id | DE-604.BV046107453 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T18:43:21Z |
| institution | BVB |
| isbn | 9780691190716 9780691190709 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-031488139 |
| oclc_num | 1119010841 |
| open_access_boolean | |
| owner | DE-11 DE-19 DE-BY-UBM |
| owner_facet | DE-11 DE-19 DE-BY-UBM |
| physical | x, 212 Seiten |
| publishDate | 2019 |
| publishDateSearch | 2019 |
| publishDateSort | 2019 |
| publisher | Princeton University Press |
| record_format | marc |
| series | Annals of mathematics studies |
| series2 | Annals of mathematics studies |
| spellingShingle | Cardaliaguet, Pierre Delarue, François 1976- Lasry, Jean-Michel Lions, Pierre-Louis 1956- The Master Equation and the Convergence Problem in Mean Field Games Annals of mathematics studies |
| title | The Master Equation and the Convergence Problem in Mean Field Games |
| title_auth | The Master Equation and the Convergence Problem in Mean Field Games |
| title_exact_search | The Master Equation and the Convergence Problem in Mean Field Games |
| title_full | The Master Equation and the Convergence Problem in Mean Field Games Pierre Cardaliaguet, François Delarue, Jean-Michel Lasry, Pierre-Louis Lions |
| title_fullStr | The Master Equation and the Convergence Problem in Mean Field Games Pierre Cardaliaguet, François Delarue, Jean-Michel Lasry, Pierre-Louis Lions |
| title_full_unstemmed | The Master Equation and the Convergence Problem in Mean Field Games Pierre Cardaliaguet, François Delarue, Jean-Michel Lasry, Pierre-Louis Lions |
| title_short | The Master Equation and the Convergence Problem in Mean Field Games |
| title_sort | the master equation and the convergence problem in mean field games |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031488139&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000991 |
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